Solve the Inequality for x (-3(x+3))/2<=6

$\frac{- 3 (x + 3)}{2} \leq 6$

Step 1

Multiply both sides by $2$ .

$\frac{- 3 (x + 3)}{2} \cdot 2 \leq 6 \cdot 2$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{- 3 (x + 3)}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{- 3 (x + 3)}{2} \cdot 2 \leq 6 \cdot 2$

Rewrite the expression.

$- 3 (x + 3) \leq 6 \cdot 2$

Apply the distributive property.

$- 3 x - 3 \cdot 3 \leq 6 \cdot 2$

Multiply $- 3$ by $3$ .

$- 3 x - 9 \leq 6 \cdot 2$

Simplify the right side.

Multiply $6$ by $2$ .

$- 3 x - 9 \leq 12$

Step 3

Solve for $x$ .

Move all terms not containing $x$ to the right side of the inequality.

Add $9$ to both sides of the inequality.

$- 3 x \leq 12 + 9$

Add $12$ and $9$ .

$- 3 x \leq 21$

Divide each term in $- 3 x \leq 21$ by $- 3$ and simplify.

Divide each term in $- 3 x \leq 21$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} \geq \frac{21}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} \geq \frac{21}{- 3}$

Divide $x$ by $1$ .

$x \geq \frac{21}{- 3}$

Simplify the right side.

Divide $21$ by $- 3$ .

$x \geq - 7$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 7$

Interval Notation:

$[- 7, \infty)$

Solve the Inequality for x (-3(x+3))/2<=6

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